Exponent Crazy

[ivy.chris]

(6.804)^6(1.701)^-13
__________________
(2)^19(3.402)^-7


The expression

(6.804)^6(1.701)^-13
_____________________
(2)^19(3.402)^-7

can be simplified as follows:

(6.804)^6(3.402)^7
_________________
(2)^19(1.701)^13

Can someone please explain which exponent property is applied to "flip" the 1.701 and 3.402 from the numerator to the denominator (and vice versa)

Thanks!

[sunny.jain]

(6.804)^6(3.402)^7
_________________
(2)^19(1.701)^13

==> (6.804)^6 * (2*3.402)^7
_______________________
2^19 * ( 4* 1.701) ^13

==> (6.804)^13 * 2^7
________________
2^19 * (6.804)^13 * 2^26

I hope its done now. Please check whether you have correctly given the first expression i used in my explanation. I copied it from you solution.

[Kweku.Amoako]

I think if you recognize that

6.804 = 2 * (3.402) = 4 * (1.701)...then the rest is easy to understand

[bluescale]

(6.804)^6(1.701)^-13
__________________
(2)^19(3.402)^-7


The expression

(6.804)^6(1.701)^-13
_____________________
(2)^19(3.402)^-7

can be simplified as follows:

(6.804)^6(3.402)^7
_________________
(2)^19(1.701)^13

Can someone please explain which exponent property is applied to "flip" the 1.701 and 3.402 from the numerator to the denominator (and vice versa)

Thanks!

You can flip 3.402^-7 from the denominator to the numerator because it is raised to a negative exponent. The same is true (in reverse) for 1.701^-13.

Keep this rule in mind at all times: When you raise a number to a negative exponent, you flip it from the numerator to the denominator, or vice versa.

Some examples:

x^-2 = 1/(x^2)
1/(x^-2) = x^2
2^-2 = 1/(2^2) = 1/4
1/(2^-2) = 2^2 = 4

I hope that helps.

[Ben Ku]

Can someone please explain which exponent property is applied to "flip" the 1.701 and 3.402 from the numerator to the denominator (and vice versa)

The relevant properties of exponents that allow you to "flip" terms are:
a^(-m) = 1 / (a^m)
1 / (a^-m) = a^m
a^m / a^n = a^m-n

Basically a negative exponent means to "flip" the term from top to bottom (or vice versa). bluescale gives some nice examples.

[DRK53]

There is one step in this problem I am also perplexed about. How is it that 4^6 simplifies to 2^12? I know they are equal, but what rule allows for this?

[tim]

if you know they are equal, then you must be aware of the rule:

4^6 = (2^2)^6 = 2^(2*6) = 2^12

make sure you are very familiar with your exponents rules..

[arthi9487]

I think if you recognize that

6.804 = 2 * (3.402) = 4 * (1.701)...then the rest is easy to understand

How is someone supposed to recognize this? Is this a standard rule somewhere in the books?

[RonPurewal]

The thought process should be, essentially, "Those weird decimal values MUST be somehow related." (If they weren't, it would be impossible to simplify the expression.)

Once you have in mind the idea that there must be some sort of relationship, it's not too hard to notice that this number is twice as big as that one, and so forth.